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The mechanics of the knee joint in relation to normal walking
J Biomerhonicr.
Vol. 3. pp. 5 I-61.
Pergam~n PRSS. 1970.
Printed in Great B&in
THE MECHANICS OF THE KNEE JOINT IN RELATION TO NORMAL WALKING* .I. B. MORRISON? Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02 139, U.S.A. Abstract- Experimental measurements of normal walking were taken using male and female subjects. The mechanics of the knee joint were simplified and defined in mathematical terms. By considering the normal knee joint to function according to the mechanical principals thus defined, the forces transmitted by the joint were calculated from the experimental data. The general mechanical concepts of knee action are outlined and the assumptions made in defining the joint ‘model’ described. The results obtained are presented and discussed in relalion to the assumptions made. INTRODUCTION
joint positions the individual ligaments become taut and to which movements of the joint they exert a restraining force, quantitative assessment of the restraining forces applied to the joint by the individual ligaments cannot be made nor can the relative importance of their role in walking be deduced. Literature describing the function of the ligaments at the knee, although abundant in nature, is often in disagreement. Brantigan and Voshell (194 I), review contradictory statements made by different authors and present the results of experiments on cadavers which assess the validity of these statements. Despite this, contradictory statements regarding the function of the ligaments continue to be made. The function of the musculature has been studied in greater detail. Much useful information regarding the function of the muscles and the phasic relationship of their activity has been obtained by the development and use of electromyography (University of California, 1953; Lippold and Bigland, 1954; Basmajian, 1962; Close, 1964). Experiments involving the electrical stimulation of muscles have greatly clarified the relationship of muscle force to muscle length and velocity of shortening (Roberts, 1967). There is yet,
studies have been carried field of joint action, investigations have in the past been mostly confined to the analysis of movement. Experiments aimed at the analysis of forces acting on the joints and in the surrounding connective tissues are few and of a limited nature. The information available on the function of the knee joint is generally derived from two sources, namely the study of normal gait, and experiments conducted on cadavers. Information obtained from the study of normal gait is limited by the difficulty of measuring accurately internal movement of the joint due to the presence of the surrounding tissue. For example, while rotations about the long axes of the femur and tibia have been recorded in gait studies, (Inman et al., 1948), the position of the long axis of rotation of the joint (taken to be parallel to the long axis of the tibia) relative to the knee joint is still obscure. Observations made by study of knee joint action in cadavers are limited in their relation to normal joint function in that the joint is not subject to the force systems arising in normal joint action. While these experiments allow the investigator to record at which ALTHOUGH out in the
many
*Received 11 April 1969. *Present address: R. N. Physiological Laboratory. Alverstoke. Hants.. England. _(I
52
J. B. MORRISON
however, little information as to the magnitude and interrelation of these quantities during normal physical activity such as walking. Forces acting across the articulating surfaces of joints have recently received much attention due to their importance in the design of internal prostheses and in the understanding of joint lubrication problems. The external force system acting at the knee joint has been measured by several researchers, Elftman (1940), Marks and Hirschberg (1958), Bresler and Frankel(l950). Total force acting across the joint, however, has not been investigated in detail prior to the prCsent study. In a previous publication by the author (1968), total force transmitted by the knee joint during level walking was stated to have a maximum value of 2-4 times body weight. Forces acting at the hip joint in level walking have been measured in normal subjects by Paul (1965) and in subjects having prosthetic replacement of the femoral head by Rydell (1966). Rydell measured maximum force at the hip of a male and female subject to be of the order of 1.8 and 3.3 times body weight respectively. Paul calculated maximum joint force to be in the range 2.3-5-8 times body weight. Experiments designed to estimate the coeficient of friction in human joints have been reported by Charnley (1959), McCutchen (1962), Bamett and Cobbold (1962), and Rydell (1966). These experiments indicate the friction coefficient to be in the range 0@02-O-04. A coefficient in this range is superior to that achieved in engineering bearings of similar structure. At this point it is appropriate to mention the controls imposed on joint moverqent by the muscles and ligaments and the natural range of these movements during normal walking. In the following section, therefore, a description of the fundamental concepts of the mechanics of knee action, upon which knowledge the present work is based, is given.
General mechanical concepts of knee action The knee is extended by the quadriceps femoris, assisted by the tensor fasciae lame. Flexion is caused by the hamstrings, assisted by gracilis and sartorius. Gastrocnemius and plantaris are also flexors of the knee. Movements of the joint in other directions are prevented mainly by the binding effect of the ligaments and the geometry of the articular surfaces. Backward gliding of the tibia relative to the femur is controlled by the posterior cruciate ligment, and forward gliding of the tibia is controlled by the anterior cruciate ligament. Most authors state that adduction of the joint is prevented by the lateral collateral ligament and the cruciate ligaments, abduction by the medial collateral ligament and the cruciate ligaments (Brantigan and Voshell, 1941; Gray’s Anatomy, 1962). Steindler (1955), however, maintains that this movement is checked entirely by the collateral ligaments. The medial collateral ligament and the cruciates, acting together, limit rotations of the femur on the tibia (i.e. about the long axis of the joint)in all positions of the joint. The lateral collateral ligament resists lateral rotation when the joint is in extension. Medial or lateral moyement of the femur on the tibia is prevented by interaction between the tibia1 intercondylar eminance and the femoral codyles, and the restraint of the ligaments. Joint movement is mainly a relative sliding motion of the opposing condyles. In the last 10-20” of extension, however, the femoral condyles roll forwards slightly on the tibia. As the radius of curvature of the femoral condyles decreases from front to back, the medio-lateral axis of the joint varies in position, depending on the angle of flexion. In normal walking, rotations about the long axis of the joint are small, having a mean range of about 9” (Inman et al., 1948). Rotation occurs in the last few degrees of extension but the exact mechanism is uncertain (Gray’s Anatomy, 1962). Steindler (1955) and Morris (1953) state that the axis of rotation lies
THE MECHANICS
closer to the medial condyles while Gray ( 1962) states that it passes through the lateral condyles. The knee resists adduction and abduction in extension, a limited movement being possible in flexion (Gray’s Anatomy, 1962). Greatest flexion of the joint during walking occurs in the swing phase and is of the order of 75” (Berry, 1952). For most of the stance phase flexion is less than 20” but increases to about 55” at toe off (Berry, 1952). Functional concepts for analysis In order to calculate the forces transmitted by the joint articulations and the connective tissues under dynamic conditions it was necessary to define the joint structure and the mechanics of its action in mathematical terms. Further, the mathematical model as constructed had to be such that a unique soiution of force actions could be calculated for any position and loading of the joint. In order to satisfy this condition and in view of the several aspects of joint mechanics not clearly defined in the literature, the joint structure and function as defined in mathematical terms involved a degree of mechanical simplification. The functional concepts adopted are described as follows. A set of reference axes X,, Y, and Z, was adopted in relation to the tibia. These axes are shown in Fig. 1. The directions of all
OF THE KNEE JOINT
53
forces acting across the knee joint were defined in terms of this system of tibial axes (see Fig. 2). The near cylindrical configuration of the femoral condyles and the relative flatness of the opposing tibia1 articulations implies approximately a line contact of surfaces in the medio-lateral direction. In the analysis a line contact was assumed and its position on the articular surfaces taken to be coincident with the Z, axis of the tibia; (Fig. 3). Anteriorposterior displacements of the line of contact from the Z, axis due to the rolling of the femoral condyles on the tibia1 condyles in extension were neglected. It was further assumed that the femoral condyles rotated relative to the tibia about a fixed centre line parallel to the Z, axis and intersecting the Y, axis of the tibia; (Fig. 1). This centre line was taken to be coincident with the axis of
Fig. 2. External force system acting at knee-expressed in terms of tibia1reference axes.
Contact ore0 between opposing yles
Lotcral
aspect
Anterior
aspect
Fig. 1. Reference axes of femur and tibia.
Fig. 3. Tibial condyles - superior aspect-showing assumed contact area of tibial and femoral condyles.
54
J. B. MORRISON
rotation of the knee joint in the position of 180” extension. Muscles and ligaments of the joint were defined by the position of their attachments and for this purpose a further two sets of axes were adopted. Axes relative to the pelvis X,, YP and Z, were assumed to have origin at the anterior superior spine of the left hip bone, and to be coincident with the intersections of the planes of the body drawn through that point. The femur was defined by axes X,, Y, and Z,, having origin at the intersection of the assumed centre line of the femoral condyles and the Y8 axis of the tibia (see Fig. 1). The Y, axis represents the mechanical axis of the femur and the Z, axis is coincident with the centre line of the condyles. The error in the assumption of a fixed point origin on the femur relative to the axes of the tibia is small, but increases with degree of flexion of the joint. The true position of the origin on the femur subject to 90” of flexion is shown in Fig. 4. A detailed discussion of this movement is given by Steindler (1955). Extension or flexion of the knee was controlled by forces acting in the quadriceps femoris, hamstrings or gastrocnemius muscle groups. As the hamstrings and gastrocnemius muscles both tend to flex the joint, electromyographic data describing muscle activity during the walking cycle was used to decide which of these two muscle groups were active at a given instant. Details of the choice
f’
Fig. 4. Centre of rotation of femur. CC’-centre of rotation at 180” extension. d,d*-centre of rotation at 90” flexion. Error in assumed fixed point origin at 90” flexion-distance CC’.
of these muscle groups and of the method of determining their force vectors relative to the tibia1 axes are given in a previous publication (Morrison, 1968). The force transmitted by the joint articulations was considered as two components, a direct compressive force R, acting in the direction of the Y, axis of the joint, and a side or shear force R, acting in the medio-lateral direction. Force R, was assumed to be transmitted partly as a friction force acting between the faces of the opposing condyles, and partly as a compressive force acting between the concave inner boundary of the tibia1 condyles and the inner boundary of the femoral condyles. The effects of friction in the joint in the anterior-posterior direction was neglected. It was therefore assumed that an anteriorly directed force on the tibia was resisted by the anterior cruciate ligament whilst a posteriorly directed force was resisted by the posterior cruciate ligament. The direction of the force imposed on the joint by a ligament was defined in terms of the positions of the ligament’s attachments relative to the tibia1 axes. Moments of adduction or abduction acting on the joint were equilibrated by a redistribution of pressure on the condyles, i.e. a displacement of the centre of pressure along the line of contact of the condyles from the joint centre. As pressure on one condyle tended to zero, further loading in this direction was resisted by a reaction in the collateral ligament of that condyle. Torsional action at the joint (i.e. about the Y, axis) was neglected. The effect of torsion on the calculations is discussed in the presentation of results. Experimental procedure and analysis In the following paragraph a brief account of experimental procedure and analysis is given. Details of this section of the investigations are presented in a previous publication (Morrison, 1968). Subjects were filmed from the front and side whilst walking along an instrumented walkway (see Fig. 5). Reaction between
THE
MECHANICS
OF THE
KNEE JOINT
boom E.M.G
2 Camera
coblas
Fig. 5. Diagram of walkway viewed along the Z, axis (above) and y. axis (below).
ground and’foot during one step was measured by a force plate. Accelerations of limb segments were calculated from measurements taken from the tine film records. The externat force system acting at the knee joint was then calculated by summing ground force and acceleration forces acting on the limb. By considering the knee joint to operate according to the mechanical principles described in the previous section and applying the experimental results to this ‘joint model’, a complete force analysis of the joint under dynamic conditions could be achieved for any position of the walking cycle. By computing forces in this manner for each consecutive frame of tine film recorded, the force cycles acting at the articular surfaces and in the muscles and ligaments were obtained.
RESULTS
The results presented describe fourteen experiments involving 3 female and 9 male subjects. All subjects were normal adults, 11 being in the age range 18-24 yr and 1 male of age 38 yr. It should be noted that where average figures are presented, to prevent bias of results towards subjects tested
more than once, the average values obtained from tests on these subjects are considered in conjunction with the values obtained in single tests on the other subjects. In the following discussion the phrase ‘joint force’ denotes the compressive force R, acting normal to the articular surfaces of the tibia. Considering component R, to be totally transmitted by the joint surfaces, the resultant values of the two force components R, and R, are of the order of O-2 per cent greater than the values of ‘joint force’ (i.e. component R,) quoted in the results. In all cases the joint force is measured as a fraction or multiple of the body weight of the subject. The complete solution of forces is presented for three subjects in Figs. 6-10. The results shown in these figures are considered to be representative of the range of results obtained. In each figure the results obtained for the three subjects are superimposed in order to indicate the degree of variation in force systems developed by different subjects performing the same activity. ( I) Muscle forces
Maximum force values in the region of 400 lb were calculated in all three muscle
56
J. B. MORRISON 5
I
I
I
I
i
0 60
60
100
20
40
60
60
FWcentag6 of cycle
walking. Test No. 11_;2_----;
Fig. 6. Joint force at knee-level
13-.-.-_.
Ouadriceps femaris
S
0 *
; S
400
S ::
200
%
Hamrtrinps
0 400 Gastrocnemius 200
.
/
0 60
60
100
20 Percentage
Fig. 7. Muscle force-level
a’p-Y <’ 40
‘\ \, 60
1 60
of cycle
walking. Test No. 11_;
groups. Mean maximum forces developed by the twelve subjects in the quadriceps femotis, hamstrings and gastrocnemius were 167, 270 and 234 lb respectively. Force actions calculated in the three muscle
\
2---_--;
13- ._.__
groups (Fig. 7) may be explained as follows. Immediately prior to heel strike, force action in the hamstrings decelerates the forwards motion of the leg. At heel strike the foot is positioned well in front of the knee and hip
THE
MECHANICS
OF THE
KNEE
JOINT
57
80 60 40
=
20 0 60 60
z 2
40 20 0
Anterior crwote
Posterior cruciote
Medlol colloterol
60 60 40 20 0
Loterol colloterol
60
60
100
20 Percentage
40
60
60
of cycle
Fig. 8. Ligament forces during level walking. Test No. I 1_;~___-;*~
_._.
50
.c
e f
s P
c
0
-50 -100
-150
-200 80
I00
20 Percentage
40
60
60
of cycle
Fig. 9. Torque M, acting at knee joint during level walking. Test No. 1 l-; 2----_: 13_-.-.-_.
i!
I
Pwcentoge of cycle
,I711
Loterol
4%
condyte
Reference
axes
Fig. 10. Position of centre of pressure Z, on condyles during level walking. Test No. 11 -: I----; 13_._.__.
58
J. B. MORRISON
joints and hence vertical force acting on the foot causes a moment, --M,, to act at both joints. In most experiments this moment was increased by the action of an anteriorly directed force on the foot at heel strike. This moment action is resisted by force action in the hamstrings which, having a biarticular function, stabilizes both the knee joint and the hip joint (assisted by the gluteal muscles). The advantage of the biarticular muscle in these circumstances is illustrated by Elftman (1941). Following heel strike the knee is subject to a moment, +M,, i.e. a tendency to flex the joint, and force action in the quadriceps femoris resists this moment and controls the position of the knee. In the second half of the stance phase, force action in the calf muscles causes plantar flexion of the ankle and hence produces forwards acceleration of the body and a corresponding anteriorly directed force acting at the foot. Moment, -M,,, acting at the knee tends to extend the joint and is resisted by the action of gastrocnemius. Being a biarticular muscle the gastrocnemius both stabilizes the knee and produces plantar flexion of the ankle (assisted by soleus). At toe-off force action in the quadriceps femoris imparts a forwards acceleration to the leg. It should be noted that in calculation of the force values acting in the hamstrings it was assumed that there was no assistance of this muscle group from the gracilis or sartorius muscles. Gracilis is mainly an adductor of the hip and its line of action affords it little leverage at the knee in comparison to the hamstring muscles. Sartorius, also having less leverage than the hamstrings, is a relatively weak muscle. it is reasonable to assume therefore that the components of transmitted by these two moment, -M,, muscles are of a minor nature and the error introduced by assuming the hamstrings group to be the sole flexor of the joint is small. The same argument may be applied to justify the assumption of the quadriceps femoris as the sole extensor of the knee,
which neglects fasciae latae.
the
assistance
of
tensor
(2) Forces in the ligaments The magnitude and phasing of the forces calculated in the ligaments is shown in Fig. 8. Maximum force recorded in the cruciate ligaments of the 12 subjects varied from 10 to 112 lb. In all tests the posterior cruciate carried the greater force, mean maximum force being 74 lb compared with 35 lb in the anterior cruciate. In calculating these forces the effect of friction was neglected. A friction force between the articular surfaces acting in the anterior or posterior direction may either increase or decrease the force required in the cruciates depending on the direction of rotation of the femoral condyles on the tibia. Assuming a value of 0.02 for the coefficient of friction in the joint, friction forces would have a maximum value of the order of 9 lb, this force corresponding to the position of maximum joint force in the walking cycle. Forces calculated to act in the medial collateral ligament were small, having a maximum value of 29 lb. Forces transmitted by the lateral collateral ligament were much greater, having a mean maximum value of 59 lb, and a maximum value’of 148 lb. These forces were developed to prevent adduction at the knee during the stance phase of walking. According to the literature surveyed (Brantigan and Voshell, 1941; Gray’s Anatomy, 1962: Eds. D. V. Davies and F. Davies), part of the reaction required to resist abduction or adduction may be transmitted by the cruciates. The experiments of Brantigan and Voshell (1941) show that when the knee is in extension the collateral ligaments are capable of preventing movement in this direction, no instability occurring when the cruciates were severed. In flexion, however, due to the slackening of the lateral collateral, absence of the cruciates resulted in increased instability of the joint. This would indicate that the assistance of the cruciates in checking abduction or adduction is more
THE
MECHANICS
OF THE
significant in positions of flexion. From a mechanical point of view the collateral ligaments are best situated to resist abduction and adduction and, provided there is no initial slackness in the ligaments, there must consequently be more strain in the collateral ligament resisting movement than in the cruciates. The large forces calculated to be acting in the lateral ligament occurred in the stance phase of walking and hence at positions of the joint in which this ligament would normally be taut. It is deduced therefore that in walking the collaterals rather than the cruciates provide the major reaction to moments of abduction or adduction acting on the joint. With regard to forces calculated in the lateral collateral, it should be noted that the forces ascribed to this ligament for the purpose of analysis. will most likely be carried partly as tension in the ilio-tibia1 tract. The distribution of force between these two elements could not be determined from the information available. It may also be possible that the large adduction force acting on the joint during the stance phase is partly equilibrated by differential action of the lateral and medial hamstrings or of the lateral and medial heads of gastrocnemius. At present however there is no experimental evidence to support this theory. It has been suggested by several authors that tension receptors in the articular ligaments, when activated, instigate a reflex contraction in the muscles capable of protecting the particular ligament. This hypothesis is suggested in relation to the ligaments of the knee joint in particular by Smillie (1946). Experiments by Stener (1959) investigating the medial collateral ligament of the knee joint contradict this hypothesis. Figure 9 shows an increasing inward acting at the knee during torque, -M,, the stance phase of walking. Moment action, M,, about the long axis of the tibia must be balanced mainly by force actions in the ligaments and will alter the distribution of ligament forces calculated in the analysis. From mechanical considerations the oblique
KNEE JOINT
59
posterior fibres of the medial collateral ligament would be most favourably placed to resist the inward torque shown in Fig. 9. and it is suggested that the greater part of the torque acting at the knee will be balanced by tension in this ligament. Tension in this ligament required to produce equilibrium would not significantly increase calculated values of joint force as force in the posterior cruciate, which is also in tension at this part of the cycle, would tend to be reduced in order to maintain equilibrium of forces in the anterior-posterior direction.
(3) Forces transmitted by the articular surfaces Joint force results presented in Fig. 6 represent the tests in which the greatest, average and smallest values of maximum joint force, R,, were obtained. The three main peaks in the joint force curve, referred to as peaks a, b and c, in Fig. 6 correspond to the peaks of muscle force shown in Fig. 7. For the 12 subjects tested the average values of peaks a, b and c were 2.43, 2-23 and 2.72 times body weight respectively. Maximum joint force measured varied between 2.06 and 4-O with an average value of 3.03 times body weight. Variations in peak values of joint force and their phasing in the walking cycle shown by different subjects are considered by the author to be due partly to anthropometric differences between subjects and partly to differing characteristics in the gait of the subjects. Where a subject was tested twice, the joint force curves obtained from the two tests bore close comparison, the magnitude of the three peaks and the percentage of the walking cycle at which they occurred being in good agreement. Tests on male and female subjects revealed no obvious differences in the magnitude or cyclic variation of joint force between the sexes. In Figs. 6-l 0 tests 11 and 13 represent the results obtained using female subjects
60
J. B. MORRISON
and test 2 represents the results obtained lateral condyle, the stresses acting in the shaft using a male subject. From the results of of the tibia would be less. the 14 experiments conducted it would SUMhlARY OF RESULTS appear that variations in joint force within the sex groups, due possibly to anthropo(1) Maximum joint force calculated at the metric factors and individual gait characterknee during walking was in the range 2-4 istics, are greater than any variations between times body weight, the average value of 12 the sexes due to anatomical differences. subjects being 3.03 times body weight. The side or shear force, R,,(measured as a (2) When the joint was highly loaded, the fraction of body weight) acting on the condyles greater portion of the load was transmitted is shown in Fig. 6. Due to its relatively small by the medial condyles. magnitude in this graph, the curves of three (3) Forces acting on the joint in the mediosubjects could not be superimposed clearly lateral direction were generally small. Their and only the curve of one subject is therefore mean maximum value was calculated to be shown. Mean maximum value of R,calculated 0.26 times body weight. for the 12 subjects was O-26 times body (4) The mean maximum forces acting in the weight. anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments Experimental results of all subjects indicated that during the stance phase of walking the were 35,74,14 and 59 lb respectively. (5) The greatest muscle force calculated was centre of pressure was positioned over the medial condyles, as shown in Fig. 10. It 405 lb. For the 12 subjects tested the average therefore follows that the greater part of the values of maximum force developed in the quardiceps femoris, hamstrings and gastrojoint force was transmitted by the medial cnemius muscle groups was 167, 270 and condyles at this part of the cycle. The above 234 lb respectively. statement is at variance with the commonly (6) No significant difference was apparent held belief that the greater load is transbetween the joint forces calculated for male mitted by the lateral condyles. Steindler and female subjects. (1955) states that the greater amount of pres(7) It is essential that the values quoted sure is borne by the lateral condyles ‘because of the obliquity of the anatomical axis of the above are interpreted in relation to the asfemur’. It is maintained by the author that the sumptions made in defining the mechanics of the knee joint. The limitations of the analysis obliquity of the axis of the femur cannot possibly affect the force system acting at the in determining the true value of these quantities are discussed in detail with the presentaknee joint, and consequently the distribution tion of results. of pressure between the condyles. The force Knowledge of the force values transmitted system acting at the knee is dependent, by the joint tissues is of importance in the rather, on the position of the centre of gravity of reconstructive joint of the body and the external forces acting further development upon it. From a mechanical point of view, a surgery, in the design of mechanical compongreater portion of the force transmitted by the ents for partial or total joint replacement, and in the understanding of joint lubrication. It is medial condyles as opposed to the lateral hoped that the work described in this paper condyles would be structurally more favourwill contribute to the solution of problems able for the following reasons: as the medial in these areas and also to the general undercondyle probably has a larger bearing surface, standing of the mechanics of the knee. the compressive stress at the articular surface would be lower; as the medial condyle Acknowledgements-The work described here was overhangs the shaft of the tibia less than the carried out at the Bio-Engineering Unit, University of
THE
MECHANICS
Strathclyde, Glasgow, and financed by the Medical Research Council. The author wishes to thank Professor R. M. Kenedi and Dr. J. P. Paul for guidance in the method of analvsis and Mr. D. N. Condie for assistance in the execution of experiments and computation of results. REFERENCES Bamett. C. H. and Cobbold, A. F. (1962) Lubrication within living joints. J. BoneJt Surg. 44B, 662. Basmajian, J. V. (1962) Muscles Alive, Their Functions Revealed by Ekctromyography. Williams and Wilkins, Baltimore. Berry, F. R. (1952) Angle variation patterns of normal hip, knee and ankle in different operations. Unit. Calif. Prosth. Dev. Res. Rep. Ser. 2, Issue 2 1. Brantigan, 0. C. and Voshell. A. F. (1941) The mechanics of the ligaments and menisci of the knee joint. J. Bone J? Surg. 23,44. Bresler, B. and Frankel, J. P. (1950) The forces and moments in the leg during level walking. Trans. Am. Sot. mech. Engrs 72.27. Charnley, J. (1959) The lubrication of animal joints. Proc. Symp. Biomechanics lnstn mech. Engrs, London, p. 12. Close, J. R. ( 1964) Motor Function in the Lower Extremity. Thomas, Springfield, Ill. Elftman, I-& (1941) The action of muscles in the body. Biol. Symp. 3, 19 1. Elftman, H. (1940) Forces and energy changes in the leg during walking. Am. J. Physiol. 129,672. Gray’s Anatomy. (1962) (Edited by D. V. Davies and F. Davies), 33rd Edn. Longmans, London.
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JOINT
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Inman, V. T. er al. (1948) Transverse rotations of the segments of the lower extremity in locomotion. J. Bone Jt Surg. %A, 859. Liooold. 0. C. and Bi&nd. B. (1954) The relation between force, velo&y and integrated electrical activity in human muscles. J. Physiof. 123,2 13. Marks, M. and Hirschberg. G. (1958) Analvsis of hemiplegic gait. Ann. N.Y. A&d. Sci. 74.59. _ McCutchen, C. W. (1962) The frictional properties of animal joints. Wear 5, I- 17. Morris, H. (1953) Human Anatomy. (Edited by J. P. Schaeffer), 1 Ith Edn. Blakiston, New York. Morrison, J. B. (1968) Bioengineering analysis of force actions transmitted by the knee joint. Bio-med. Engng 3, 164. Paul, J. P. (1965). Bioengineering studies of the forces transmitted by joints-II. Biomechanics and Related Bioengineerina Topics. (Edited by R. M. Kenedi). p. 369: Pergamon Press. Oxford. _ Roberts, T. D. M. (1967) Neurophysiology of Postural Mechanisms. Plenum, New York. Rydell. N. (1966) Forces Acting on the Femoral Head Prothesis. (Edited by A. B. Tryckeri), Litotyp. Gotenburg, Sweden. Smillie. 1. S. (1946) Iqjuries of the Knee Joint. Livingstone, Edinburgh. Steindler. A. ( 1955) Kinesiofogy. Thomas, Springfield, Ill. Stener, B. (1959) Experimental evaluation of the hypothesis of ligamento-muscular protective reflexes. Actu. phys. stand. 48, Suppl. 166. University of California (1953) The pattern of muscular activity in the lower extremity during walking. Univ. Cal$ Prosrh. Dev. Res. Rep. Ser. 2, Issue 25.
Vol. 3. pp. 5 I-61.
Pergam~n PRSS. 1970.
Printed in Great B&in
THE MECHANICS OF THE KNEE JOINT IN RELATION TO NORMAL WALKING* .I. B. MORRISON? Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02 139, U.S.A. Abstract- Experimental measurements of normal walking were taken using male and female subjects. The mechanics of the knee joint were simplified and defined in mathematical terms. By considering the normal knee joint to function according to the mechanical principals thus defined, the forces transmitted by the joint were calculated from the experimental data. The general mechanical concepts of knee action are outlined and the assumptions made in defining the joint ‘model’ described. The results obtained are presented and discussed in relalion to the assumptions made. INTRODUCTION
joint positions the individual ligaments become taut and to which movements of the joint they exert a restraining force, quantitative assessment of the restraining forces applied to the joint by the individual ligaments cannot be made nor can the relative importance of their role in walking be deduced. Literature describing the function of the ligaments at the knee, although abundant in nature, is often in disagreement. Brantigan and Voshell (194 I), review contradictory statements made by different authors and present the results of experiments on cadavers which assess the validity of these statements. Despite this, contradictory statements regarding the function of the ligaments continue to be made. The function of the musculature has been studied in greater detail. Much useful information regarding the function of the muscles and the phasic relationship of their activity has been obtained by the development and use of electromyography (University of California, 1953; Lippold and Bigland, 1954; Basmajian, 1962; Close, 1964). Experiments involving the electrical stimulation of muscles have greatly clarified the relationship of muscle force to muscle length and velocity of shortening (Roberts, 1967). There is yet,
studies have been carried field of joint action, investigations have in the past been mostly confined to the analysis of movement. Experiments aimed at the analysis of forces acting on the joints and in the surrounding connective tissues are few and of a limited nature. The information available on the function of the knee joint is generally derived from two sources, namely the study of normal gait, and experiments conducted on cadavers. Information obtained from the study of normal gait is limited by the difficulty of measuring accurately internal movement of the joint due to the presence of the surrounding tissue. For example, while rotations about the long axes of the femur and tibia have been recorded in gait studies, (Inman et al., 1948), the position of the long axis of rotation of the joint (taken to be parallel to the long axis of the tibia) relative to the knee joint is still obscure. Observations made by study of knee joint action in cadavers are limited in their relation to normal joint function in that the joint is not subject to the force systems arising in normal joint action. While these experiments allow the investigator to record at which ALTHOUGH out in the
many
*Received 11 April 1969. *Present address: R. N. Physiological Laboratory. Alverstoke. Hants.. England. _(I
52
J. B. MORRISON
however, little information as to the magnitude and interrelation of these quantities during normal physical activity such as walking. Forces acting across the articulating surfaces of joints have recently received much attention due to their importance in the design of internal prostheses and in the understanding of joint lubrication problems. The external force system acting at the knee joint has been measured by several researchers, Elftman (1940), Marks and Hirschberg (1958), Bresler and Frankel(l950). Total force acting across the joint, however, has not been investigated in detail prior to the prCsent study. In a previous publication by the author (1968), total force transmitted by the knee joint during level walking was stated to have a maximum value of 2-4 times body weight. Forces acting at the hip joint in level walking have been measured in normal subjects by Paul (1965) and in subjects having prosthetic replacement of the femoral head by Rydell (1966). Rydell measured maximum force at the hip of a male and female subject to be of the order of 1.8 and 3.3 times body weight respectively. Paul calculated maximum joint force to be in the range 2.3-5-8 times body weight. Experiments designed to estimate the coeficient of friction in human joints have been reported by Charnley (1959), McCutchen (1962), Bamett and Cobbold (1962), and Rydell (1966). These experiments indicate the friction coefficient to be in the range 0@02-O-04. A coefficient in this range is superior to that achieved in engineering bearings of similar structure. At this point it is appropriate to mention the controls imposed on joint moverqent by the muscles and ligaments and the natural range of these movements during normal walking. In the following section, therefore, a description of the fundamental concepts of the mechanics of knee action, upon which knowledge the present work is based, is given.
General mechanical concepts of knee action The knee is extended by the quadriceps femoris, assisted by the tensor fasciae lame. Flexion is caused by the hamstrings, assisted by gracilis and sartorius. Gastrocnemius and plantaris are also flexors of the knee. Movements of the joint in other directions are prevented mainly by the binding effect of the ligaments and the geometry of the articular surfaces. Backward gliding of the tibia relative to the femur is controlled by the posterior cruciate ligment, and forward gliding of the tibia is controlled by the anterior cruciate ligament. Most authors state that adduction of the joint is prevented by the lateral collateral ligament and the cruciate ligaments, abduction by the medial collateral ligament and the cruciate ligaments (Brantigan and Voshell, 1941; Gray’s Anatomy, 1962). Steindler (1955), however, maintains that this movement is checked entirely by the collateral ligaments. The medial collateral ligament and the cruciates, acting together, limit rotations of the femur on the tibia (i.e. about the long axis of the joint)in all positions of the joint. The lateral collateral ligament resists lateral rotation when the joint is in extension. Medial or lateral moyement of the femur on the tibia is prevented by interaction between the tibia1 intercondylar eminance and the femoral codyles, and the restraint of the ligaments. Joint movement is mainly a relative sliding motion of the opposing condyles. In the last 10-20” of extension, however, the femoral condyles roll forwards slightly on the tibia. As the radius of curvature of the femoral condyles decreases from front to back, the medio-lateral axis of the joint varies in position, depending on the angle of flexion. In normal walking, rotations about the long axis of the joint are small, having a mean range of about 9” (Inman et al., 1948). Rotation occurs in the last few degrees of extension but the exact mechanism is uncertain (Gray’s Anatomy, 1962). Steindler (1955) and Morris (1953) state that the axis of rotation lies
THE MECHANICS
closer to the medial condyles while Gray ( 1962) states that it passes through the lateral condyles. The knee resists adduction and abduction in extension, a limited movement being possible in flexion (Gray’s Anatomy, 1962). Greatest flexion of the joint during walking occurs in the swing phase and is of the order of 75” (Berry, 1952). For most of the stance phase flexion is less than 20” but increases to about 55” at toe off (Berry, 1952). Functional concepts for analysis In order to calculate the forces transmitted by the joint articulations and the connective tissues under dynamic conditions it was necessary to define the joint structure and the mechanics of its action in mathematical terms. Further, the mathematical model as constructed had to be such that a unique soiution of force actions could be calculated for any position and loading of the joint. In order to satisfy this condition and in view of the several aspects of joint mechanics not clearly defined in the literature, the joint structure and function as defined in mathematical terms involved a degree of mechanical simplification. The functional concepts adopted are described as follows. A set of reference axes X,, Y, and Z, was adopted in relation to the tibia. These axes are shown in Fig. 1. The directions of all
OF THE KNEE JOINT
53
forces acting across the knee joint were defined in terms of this system of tibial axes (see Fig. 2). The near cylindrical configuration of the femoral condyles and the relative flatness of the opposing tibia1 articulations implies approximately a line contact of surfaces in the medio-lateral direction. In the analysis a line contact was assumed and its position on the articular surfaces taken to be coincident with the Z, axis of the tibia; (Fig. 3). Anteriorposterior displacements of the line of contact from the Z, axis due to the rolling of the femoral condyles on the tibia1 condyles in extension were neglected. It was further assumed that the femoral condyles rotated relative to the tibia about a fixed centre line parallel to the Z, axis and intersecting the Y, axis of the tibia; (Fig. 1). This centre line was taken to be coincident with the axis of
Fig. 2. External force system acting at knee-expressed in terms of tibia1reference axes.
Contact ore0 between opposing yles
Lotcral
aspect
Anterior
aspect
Fig. 1. Reference axes of femur and tibia.
Fig. 3. Tibial condyles - superior aspect-showing assumed contact area of tibial and femoral condyles.
54
J. B. MORRISON
rotation of the knee joint in the position of 180” extension. Muscles and ligaments of the joint were defined by the position of their attachments and for this purpose a further two sets of axes were adopted. Axes relative to the pelvis X,, YP and Z, were assumed to have origin at the anterior superior spine of the left hip bone, and to be coincident with the intersections of the planes of the body drawn through that point. The femur was defined by axes X,, Y, and Z,, having origin at the intersection of the assumed centre line of the femoral condyles and the Y8 axis of the tibia (see Fig. 1). The Y, axis represents the mechanical axis of the femur and the Z, axis is coincident with the centre line of the condyles. The error in the assumption of a fixed point origin on the femur relative to the axes of the tibia is small, but increases with degree of flexion of the joint. The true position of the origin on the femur subject to 90” of flexion is shown in Fig. 4. A detailed discussion of this movement is given by Steindler (1955). Extension or flexion of the knee was controlled by forces acting in the quadriceps femoris, hamstrings or gastrocnemius muscle groups. As the hamstrings and gastrocnemius muscles both tend to flex the joint, electromyographic data describing muscle activity during the walking cycle was used to decide which of these two muscle groups were active at a given instant. Details of the choice
f’
Fig. 4. Centre of rotation of femur. CC’-centre of rotation at 180” extension. d,d*-centre of rotation at 90” flexion. Error in assumed fixed point origin at 90” flexion-distance CC’.
of these muscle groups and of the method of determining their force vectors relative to the tibia1 axes are given in a previous publication (Morrison, 1968). The force transmitted by the joint articulations was considered as two components, a direct compressive force R, acting in the direction of the Y, axis of the joint, and a side or shear force R, acting in the medio-lateral direction. Force R, was assumed to be transmitted partly as a friction force acting between the faces of the opposing condyles, and partly as a compressive force acting between the concave inner boundary of the tibia1 condyles and the inner boundary of the femoral condyles. The effects of friction in the joint in the anterior-posterior direction was neglected. It was therefore assumed that an anteriorly directed force on the tibia was resisted by the anterior cruciate ligament whilst a posteriorly directed force was resisted by the posterior cruciate ligament. The direction of the force imposed on the joint by a ligament was defined in terms of the positions of the ligament’s attachments relative to the tibia1 axes. Moments of adduction or abduction acting on the joint were equilibrated by a redistribution of pressure on the condyles, i.e. a displacement of the centre of pressure along the line of contact of the condyles from the joint centre. As pressure on one condyle tended to zero, further loading in this direction was resisted by a reaction in the collateral ligament of that condyle. Torsional action at the joint (i.e. about the Y, axis) was neglected. The effect of torsion on the calculations is discussed in the presentation of results. Experimental procedure and analysis In the following paragraph a brief account of experimental procedure and analysis is given. Details of this section of the investigations are presented in a previous publication (Morrison, 1968). Subjects were filmed from the front and side whilst walking along an instrumented walkway (see Fig. 5). Reaction between
THE
MECHANICS
OF THE
KNEE JOINT
boom E.M.G
2 Camera
coblas
Fig. 5. Diagram of walkway viewed along the Z, axis (above) and y. axis (below).
ground and’foot during one step was measured by a force plate. Accelerations of limb segments were calculated from measurements taken from the tine film records. The externat force system acting at the knee joint was then calculated by summing ground force and acceleration forces acting on the limb. By considering the knee joint to operate according to the mechanical principles described in the previous section and applying the experimental results to this ‘joint model’, a complete force analysis of the joint under dynamic conditions could be achieved for any position of the walking cycle. By computing forces in this manner for each consecutive frame of tine film recorded, the force cycles acting at the articular surfaces and in the muscles and ligaments were obtained.
RESULTS
The results presented describe fourteen experiments involving 3 female and 9 male subjects. All subjects were normal adults, 11 being in the age range 18-24 yr and 1 male of age 38 yr. It should be noted that where average figures are presented, to prevent bias of results towards subjects tested
more than once, the average values obtained from tests on these subjects are considered in conjunction with the values obtained in single tests on the other subjects. In the following discussion the phrase ‘joint force’ denotes the compressive force R, acting normal to the articular surfaces of the tibia. Considering component R, to be totally transmitted by the joint surfaces, the resultant values of the two force components R, and R, are of the order of O-2 per cent greater than the values of ‘joint force’ (i.e. component R,) quoted in the results. In all cases the joint force is measured as a fraction or multiple of the body weight of the subject. The complete solution of forces is presented for three subjects in Figs. 6-10. The results shown in these figures are considered to be representative of the range of results obtained. In each figure the results obtained for the three subjects are superimposed in order to indicate the degree of variation in force systems developed by different subjects performing the same activity. ( I) Muscle forces
Maximum force values in the region of 400 lb were calculated in all three muscle
56
J. B. MORRISON 5
I
I
I
I
i
0 60
60
100
20
40
60
60
FWcentag6 of cycle
walking. Test No. 11_;2_----;
Fig. 6. Joint force at knee-level
13-.-.-_.
Ouadriceps femaris
S
0 *
; S
400
S ::
200
%
Hamrtrinps
0 400 Gastrocnemius 200
.
/
0 60
60
100
20 Percentage
Fig. 7. Muscle force-level
a’p-Y <’ 40
‘\ \, 60
1 60
of cycle
walking. Test No. 11_;
groups. Mean maximum forces developed by the twelve subjects in the quadriceps femotis, hamstrings and gastrocnemius were 167, 270 and 234 lb respectively. Force actions calculated in the three muscle
\
2---_--;
13- ._.__
groups (Fig. 7) may be explained as follows. Immediately prior to heel strike, force action in the hamstrings decelerates the forwards motion of the leg. At heel strike the foot is positioned well in front of the knee and hip
THE
MECHANICS
OF THE
KNEE
JOINT
57
80 60 40
=
20 0 60 60
z 2
40 20 0
Anterior crwote
Posterior cruciote
Medlol colloterol
60 60 40 20 0
Loterol colloterol
60
60
100
20 Percentage
40
60
60
of cycle
Fig. 8. Ligament forces during level walking. Test No. I 1_;~___-;*~
_._.
50
.c
e f
s P
c
0
-50 -100
-150
-200 80
I00
20 Percentage
40
60
60
of cycle
Fig. 9. Torque M, acting at knee joint during level walking. Test No. 1 l-; 2----_: 13_-.-.-_.
i!
I
Pwcentoge of cycle
,I711
Loterol
4%
condyte
Reference
axes
Fig. 10. Position of centre of pressure Z, on condyles during level walking. Test No. 11 -: I----; 13_._.__.
58
J. B. MORRISON
joints and hence vertical force acting on the foot causes a moment, --M,, to act at both joints. In most experiments this moment was increased by the action of an anteriorly directed force on the foot at heel strike. This moment action is resisted by force action in the hamstrings which, having a biarticular function, stabilizes both the knee joint and the hip joint (assisted by the gluteal muscles). The advantage of the biarticular muscle in these circumstances is illustrated by Elftman (1941). Following heel strike the knee is subject to a moment, +M,, i.e. a tendency to flex the joint, and force action in the quadriceps femoris resists this moment and controls the position of the knee. In the second half of the stance phase, force action in the calf muscles causes plantar flexion of the ankle and hence produces forwards acceleration of the body and a corresponding anteriorly directed force acting at the foot. Moment, -M,,, acting at the knee tends to extend the joint and is resisted by the action of gastrocnemius. Being a biarticular muscle the gastrocnemius both stabilizes the knee and produces plantar flexion of the ankle (assisted by soleus). At toe-off force action in the quadriceps femoris imparts a forwards acceleration to the leg. It should be noted that in calculation of the force values acting in the hamstrings it was assumed that there was no assistance of this muscle group from the gracilis or sartorius muscles. Gracilis is mainly an adductor of the hip and its line of action affords it little leverage at the knee in comparison to the hamstring muscles. Sartorius, also having less leverage than the hamstrings, is a relatively weak muscle. it is reasonable to assume therefore that the components of transmitted by these two moment, -M,, muscles are of a minor nature and the error introduced by assuming the hamstrings group to be the sole flexor of the joint is small. The same argument may be applied to justify the assumption of the quadriceps femoris as the sole extensor of the knee,
which neglects fasciae latae.
the
assistance
of
tensor
(2) Forces in the ligaments The magnitude and phasing of the forces calculated in the ligaments is shown in Fig. 8. Maximum force recorded in the cruciate ligaments of the 12 subjects varied from 10 to 112 lb. In all tests the posterior cruciate carried the greater force, mean maximum force being 74 lb compared with 35 lb in the anterior cruciate. In calculating these forces the effect of friction was neglected. A friction force between the articular surfaces acting in the anterior or posterior direction may either increase or decrease the force required in the cruciates depending on the direction of rotation of the femoral condyles on the tibia. Assuming a value of 0.02 for the coefficient of friction in the joint, friction forces would have a maximum value of the order of 9 lb, this force corresponding to the position of maximum joint force in the walking cycle. Forces calculated to act in the medial collateral ligament were small, having a maximum value of 29 lb. Forces transmitted by the lateral collateral ligament were much greater, having a mean maximum value of 59 lb, and a maximum value’of 148 lb. These forces were developed to prevent adduction at the knee during the stance phase of walking. According to the literature surveyed (Brantigan and Voshell, 1941; Gray’s Anatomy, 1962: Eds. D. V. Davies and F. Davies), part of the reaction required to resist abduction or adduction may be transmitted by the cruciates. The experiments of Brantigan and Voshell (1941) show that when the knee is in extension the collateral ligaments are capable of preventing movement in this direction, no instability occurring when the cruciates were severed. In flexion, however, due to the slackening of the lateral collateral, absence of the cruciates resulted in increased instability of the joint. This would indicate that the assistance of the cruciates in checking abduction or adduction is more
THE
MECHANICS
OF THE
significant in positions of flexion. From a mechanical point of view the collateral ligaments are best situated to resist abduction and adduction and, provided there is no initial slackness in the ligaments, there must consequently be more strain in the collateral ligament resisting movement than in the cruciates. The large forces calculated to be acting in the lateral ligament occurred in the stance phase of walking and hence at positions of the joint in which this ligament would normally be taut. It is deduced therefore that in walking the collaterals rather than the cruciates provide the major reaction to moments of abduction or adduction acting on the joint. With regard to forces calculated in the lateral collateral, it should be noted that the forces ascribed to this ligament for the purpose of analysis. will most likely be carried partly as tension in the ilio-tibia1 tract. The distribution of force between these two elements could not be determined from the information available. It may also be possible that the large adduction force acting on the joint during the stance phase is partly equilibrated by differential action of the lateral and medial hamstrings or of the lateral and medial heads of gastrocnemius. At present however there is no experimental evidence to support this theory. It has been suggested by several authors that tension receptors in the articular ligaments, when activated, instigate a reflex contraction in the muscles capable of protecting the particular ligament. This hypothesis is suggested in relation to the ligaments of the knee joint in particular by Smillie (1946). Experiments by Stener (1959) investigating the medial collateral ligament of the knee joint contradict this hypothesis. Figure 9 shows an increasing inward acting at the knee during torque, -M,, the stance phase of walking. Moment action, M,, about the long axis of the tibia must be balanced mainly by force actions in the ligaments and will alter the distribution of ligament forces calculated in the analysis. From mechanical considerations the oblique
KNEE JOINT
59
posterior fibres of the medial collateral ligament would be most favourably placed to resist the inward torque shown in Fig. 9. and it is suggested that the greater part of the torque acting at the knee will be balanced by tension in this ligament. Tension in this ligament required to produce equilibrium would not significantly increase calculated values of joint force as force in the posterior cruciate, which is also in tension at this part of the cycle, would tend to be reduced in order to maintain equilibrium of forces in the anterior-posterior direction.
(3) Forces transmitted by the articular surfaces Joint force results presented in Fig. 6 represent the tests in which the greatest, average and smallest values of maximum joint force, R,, were obtained. The three main peaks in the joint force curve, referred to as peaks a, b and c, in Fig. 6 correspond to the peaks of muscle force shown in Fig. 7. For the 12 subjects tested the average values of peaks a, b and c were 2.43, 2-23 and 2.72 times body weight respectively. Maximum joint force measured varied between 2.06 and 4-O with an average value of 3.03 times body weight. Variations in peak values of joint force and their phasing in the walking cycle shown by different subjects are considered by the author to be due partly to anthropometric differences between subjects and partly to differing characteristics in the gait of the subjects. Where a subject was tested twice, the joint force curves obtained from the two tests bore close comparison, the magnitude of the three peaks and the percentage of the walking cycle at which they occurred being in good agreement. Tests on male and female subjects revealed no obvious differences in the magnitude or cyclic variation of joint force between the sexes. In Figs. 6-l 0 tests 11 and 13 represent the results obtained using female subjects
60
J. B. MORRISON
and test 2 represents the results obtained lateral condyle, the stresses acting in the shaft using a male subject. From the results of of the tibia would be less. the 14 experiments conducted it would SUMhlARY OF RESULTS appear that variations in joint force within the sex groups, due possibly to anthropo(1) Maximum joint force calculated at the metric factors and individual gait characterknee during walking was in the range 2-4 istics, are greater than any variations between times body weight, the average value of 12 the sexes due to anatomical differences. subjects being 3.03 times body weight. The side or shear force, R,,(measured as a (2) When the joint was highly loaded, the fraction of body weight) acting on the condyles greater portion of the load was transmitted is shown in Fig. 6. Due to its relatively small by the medial condyles. magnitude in this graph, the curves of three (3) Forces acting on the joint in the mediosubjects could not be superimposed clearly lateral direction were generally small. Their and only the curve of one subject is therefore mean maximum value was calculated to be shown. Mean maximum value of R,calculated 0.26 times body weight. for the 12 subjects was O-26 times body (4) The mean maximum forces acting in the weight. anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments Experimental results of all subjects indicated that during the stance phase of walking the were 35,74,14 and 59 lb respectively. (5) The greatest muscle force calculated was centre of pressure was positioned over the medial condyles, as shown in Fig. 10. It 405 lb. For the 12 subjects tested the average therefore follows that the greater part of the values of maximum force developed in the quardiceps femoris, hamstrings and gastrojoint force was transmitted by the medial cnemius muscle groups was 167, 270 and condyles at this part of the cycle. The above 234 lb respectively. statement is at variance with the commonly (6) No significant difference was apparent held belief that the greater load is transbetween the joint forces calculated for male mitted by the lateral condyles. Steindler and female subjects. (1955) states that the greater amount of pres(7) It is essential that the values quoted sure is borne by the lateral condyles ‘because of the obliquity of the anatomical axis of the above are interpreted in relation to the asfemur’. It is maintained by the author that the sumptions made in defining the mechanics of the knee joint. The limitations of the analysis obliquity of the axis of the femur cannot possibly affect the force system acting at the in determining the true value of these quantities are discussed in detail with the presentaknee joint, and consequently the distribution tion of results. of pressure between the condyles. The force Knowledge of the force values transmitted system acting at the knee is dependent, by the joint tissues is of importance in the rather, on the position of the centre of gravity of reconstructive joint of the body and the external forces acting further development upon it. From a mechanical point of view, a surgery, in the design of mechanical compongreater portion of the force transmitted by the ents for partial or total joint replacement, and in the understanding of joint lubrication. It is medial condyles as opposed to the lateral hoped that the work described in this paper condyles would be structurally more favourwill contribute to the solution of problems able for the following reasons: as the medial in these areas and also to the general undercondyle probably has a larger bearing surface, standing of the mechanics of the knee. the compressive stress at the articular surface would be lower; as the medial condyle Acknowledgements-The work described here was overhangs the shaft of the tibia less than the carried out at the Bio-Engineering Unit, University of
THE
MECHANICS
Strathclyde, Glasgow, and financed by the Medical Research Council. The author wishes to thank Professor R. M. Kenedi and Dr. J. P. Paul for guidance in the method of analvsis and Mr. D. N. Condie for assistance in the execution of experiments and computation of results. REFERENCES Bamett. C. H. and Cobbold, A. F. (1962) Lubrication within living joints. J. BoneJt Surg. 44B, 662. Basmajian, J. V. (1962) Muscles Alive, Their Functions Revealed by Ekctromyography. Williams and Wilkins, Baltimore. Berry, F. R. (1952) Angle variation patterns of normal hip, knee and ankle in different operations. Unit. Calif. Prosth. Dev. Res. Rep. Ser. 2, Issue 2 1. Brantigan, 0. C. and Voshell. A. F. (1941) The mechanics of the ligaments and menisci of the knee joint. J. Bone J? Surg. 23,44. Bresler, B. and Frankel, J. P. (1950) The forces and moments in the leg during level walking. Trans. Am. Sot. mech. Engrs 72.27. Charnley, J. (1959) The lubrication of animal joints. Proc. Symp. Biomechanics lnstn mech. Engrs, London, p. 12. Close, J. R. ( 1964) Motor Function in the Lower Extremity. Thomas, Springfield, Ill. Elftman, I-& (1941) The action of muscles in the body. Biol. Symp. 3, 19 1. Elftman, H. (1940) Forces and energy changes in the leg during walking. Am. J. Physiol. 129,672. Gray’s Anatomy. (1962) (Edited by D. V. Davies and F. Davies), 33rd Edn. Longmans, London.
OF THE
KNEE
JOINT
61
Inman, V. T. er al. (1948) Transverse rotations of the segments of the lower extremity in locomotion. J. Bone Jt Surg. %A, 859. Liooold. 0. C. and Bi&nd. B. (1954) The relation between force, velo&y and integrated electrical activity in human muscles. J. Physiof. 123,2 13. Marks, M. and Hirschberg. G. (1958) Analvsis of hemiplegic gait. Ann. N.Y. A&d. Sci. 74.59. _ McCutchen, C. W. (1962) The frictional properties of animal joints. Wear 5, I- 17. Morris, H. (1953) Human Anatomy. (Edited by J. P. Schaeffer), 1 Ith Edn. Blakiston, New York. Morrison, J. B. (1968) Bioengineering analysis of force actions transmitted by the knee joint. Bio-med. Engng 3, 164. Paul, J. P. (1965). Bioengineering studies of the forces transmitted by joints-II. Biomechanics and Related Bioengineerina Topics. (Edited by R. M. Kenedi). p. 369: Pergamon Press. Oxford. _ Roberts, T. D. M. (1967) Neurophysiology of Postural Mechanisms. Plenum, New York. Rydell. N. (1966) Forces Acting on the Femoral Head Prothesis. (Edited by A. B. Tryckeri), Litotyp. Gotenburg, Sweden. Smillie. 1. S. (1946) Iqjuries of the Knee Joint. Livingstone, Edinburgh. Steindler. A. ( 1955) Kinesiofogy. Thomas, Springfield, Ill. Stener, B. (1959) Experimental evaluation of the hypothesis of ligamento-muscular protective reflexes. Actu. phys. stand. 48, Suppl. 166. University of California (1953) The pattern of muscular activity in the lower extremity during walking. Univ. Cal$ Prosrh. Dev. Res. Rep. Ser. 2, Issue 25.